Phase transitions in Pareto optimal complex networks

The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their topological structure can be diverse, resulting from different mechanisms including multiplicative processes and optimization. In spatial networks or in graphs where cost constraints are at work, as it occurs in a plethora of situations from power grids to the wiring of neurons in the brain, optimization plays an important part in shaping their organization. In this paper we study network designs resulting from a Pareto optimization process, where different simultaneous constraints are the targets of selection. We analyze three variations on a problem finding phase transitions of different kinds. Distinct phases are associated to different arrangements of the connections; but the need of drastic topological changes does not determine the presence, nor the nature of the phase transitions encountered. Instead, the functions under optimization do play a determinant role. This reinforces the view that phase transitions do not arise from intrinsic properties of a system alone, but from the interplay of that system with its external constraints.Comment: 14 pages, 7 figure

A multiobjective optimization approach to statistical mechanics

Optimization problems have been the subject of statistical physics approximations. A specially relevant and general scenario is provided by optimization methods considering tradeoffs between cost and efficiency, where optimal solutions involve a compromise between both. The theory of Pareto (or multi objective) optimization provides a general framework to explore these problems and find the space of possible solutions compatible with the underlying tradeoffs, known as the {\em Pareto front}. Conflicts between constraints can lead to complex landscapes of Pareto optimal solutions with interesting implications in economy, engineering, or evolutionary biology. Despite their disparate nature, here we show how the structure of the Pareto front uncovers profound universal features that can be understood in the context of thermodynamics. In particular, our study reveals that different fronts are connected to different classes of phase transitions, which we can define robustly, along with critical points and thermodynamic potentials. These equivalences are illustrated with classic thermodynamic examples.Comment: 14 pages, 8 figure

The connection between the heat storage capability of PCM as a material property and their performance in real scale applications

Using phase change materials (PCM) for Thermal Energy Storage, the most important material property is their heat storage capability, usually given as h(T). Ideally, h(T) changes suddenly at a single temperature. However, many PCM change phase in a temperature range and show hysteresis. In addition, experience shows that even measurements with the same device on the same material can give different results when the heating rate, the amount of sample mass or the equipment device are varied. The question thus arises how to deal with different h(T) results when trying to predict the performance of a real scale application. This paper identifies the main origins of these effects and gives strategies for dealing with them.The research leading to these results has received funding from the European Commission Seventh Framework Programme (FP/2007-2013) under grant agreement n° PIRSES-GA-2013-610692 (INNOSTORAGE) and from the European Union’s Horizon 2020 research and innovation program under grant agreement No 657466 (INPATH-TES). The authors would like to thank the Catalan Government for the quality accreditation given to their research groups GREA (2014 SGR 123) and DIOPMA (2014 SGR 1543). GREA and DIOPMA are certified agents TECNIO in the category of technology developers from the Government of Catalonia. This work has been partially funded by the Spanish government (ENE2015-64117-C5-1-R (MINECO/FEDER)). Dr. Camila Barreneche and Dr. Aran Solé would like to thank Ministerio de Economía y Competitividad de España for Grant Juan de la Cierva, FJCI-2014-22886 and FJCI-2015-25741, respectively

Analysis of strain localization with a nonlocal plasticity model

In the present paper a nonlocal plasticity model is described, intended to reproduce the mechanical behaviour of stiff fine-grained soils, including the objective simulation of strain localization; the phenomenon of accumulation of deformations in narrow zones in the form of shear bands or fractures. A number of analyses have been performed to assess the developed formulation. Relevant aspects have been addressed such as the thickness of the shear band, its orientation, and the onset of localization in a boundary value problem (BVP). Results provide useful insigths into relevant aspects of the numerical simulation of strain localization

Coupled THM analysis of long-term anisotropic convergence in the full-scale micro tunnel excavated in the Callovo-Oxfordian argillite

The main purpose of this paper is to analyse the convergence measurements of the ALC1604 in situ heating test carried out in the Callovo-Oxfordian claystone formation (COx) in the Meuse/Haute-Marne underground research laboratory (MHM URL). The concept of the test consists of horizontal micro-tunnel, equipped with a steel casing. The micro-tunnel is excavated in the direction of the horizontal principal major stress (sH). In situ observations showed anisotropic convergence with the maximum and minimum values in the horizontal and vertical directions, respectively. Coupled THM numerical analyses have been carried out to provide a structured framework for interpretation, and to enhance understanding of THM behaviour of Callovo-Oxfordian claystone. However, a special mechanical constitutive law is adopted for the description of the time-dependent anisotropic behaviour of the COx. The simulation of the test using this enhanced model provides a satisfactory reproduction of the THM long-term anisotropic convergence results. It also provides a better understanding of the observed test response.Postprint (published version